How to emulate context menu key when there's none on keyboard?

I think you're looking for Shift + F10.

EDIT: Some smaller keyboards require you to use the Fn key in combination with F1 - F12 to use them. Most of the time you can 'function lock' with Fn + CapsLock or change the default behavior of the F keys in the BIOS.

The button you're referring to is called the 'Menu key' btw.

You can use AutoHotKey to remap the menu key to another key on your keyboard (even without having the key on your keyboard).

I detest the Caps Lock key, so I would use that instead:

Install AHK, and create a notepad file, ending with .ahk, containing:

CapsLock::AppsKey

This triggers the menu key (AppsKey) when the caps lock button is pressed.

If you don't want to use the Caps Lock key, see here for a list of keys AHK supports.